Group divisible designs with block size 4 and group sizes 2 and 5

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2022-03-15 DOI:10.1002/jcd.21830

R. Julian R. Abel, Thomas Britz, Yudhistira A. Bunjamin, Diana Combe

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引用次数: 4

Abstract

In this paper we provide a 4-GDD of type $2^{2} 5^{5}$ , thereby solving the existence question for the last remaining feasible type for a 4-GDD with no more than 30 points. We then show that 4-GDDs of type $2^{t} 5^{s}$ exist for all but a finite specified set of feasible pairs $(t, s)$ .

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块大小为4、组大小为2和5的可分组设计

在本文中，我们提供了一个类型为2 2 5 5${2}^{2}{5}^{5}$的4-GDD，从而解决了不超过30分的4-GDD的最后一个剩余可行类型的存在性问题。然后我们证明了类型为2 t 5 s$｛2｝^｛t｝｛5｝^｝s｝$的4-GDD存在于除有限的指定可行对集之外的所有可行对（t，s）$（t，s）$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.